17. One thousand raffle tickets are sold for $4.00 each. One grand prize of $800 and two consolation prizes of $100 each will be awarded. Jeremy purchases one ticket. Find his expected value.

Question

chris · Answer

There are 4 possible outcomes with different probabilities for Jeremy

chris · Answer

you want to add the outcomes*probability of outcome together to get the expected value

chris · Answer

1.  There is a 1/1000 chance that Jeremy wins the grand prize of $800, for a total of $800-$4 (purchase price) win - $796
2.  There is a 1/1000 chance that Jeremy wins the consolation prize of $100 - $96 profit
3.  There is a 1/1000 chance that Jeremy wins the consolation prize of $100 (the second one) - $96 profit
4.  There is a 997/1000 chance that Jeremy just loses $4

chris · Answer

So the expected value for Jeremy is 1/1000 * 796 + 2/1000 * 96 + 997/1000 * -4

anonymous · Answer

I wish that I understood this stuff like you do

chris · Answer

Well, so that comes out to -$3 - Jeremy can expect to lose $3 by spending $4 on the ticket

chris · Answer

All expected value means, is that considering the likely hood of ALL outcomes (with outcomes meaning you how much you make depending on how it turns out/luck of the draw), how much can you expect to make if you add them all up?  If I have a 10% chance of winning $100 - then I have an expected value of $10.  If I have a 10% chance of winning 100, but ALSO a 10% chance of winning 200 - then in total I can expect to win 10%of100 + 10% of 200 + 80%of0 = $30.  The point is that "ALL OUTCOMES" adds up to 100% chance - I must have one of those outcomes, so all I need to do for the overall expected value is add up the expected value of each individual outcome

chris · Answer

The reason I subtracted $4 from each of the possibly outcomes (e.g. the grand prize of 800), is that I've already spent $4 on the ticket itself - so really I'm only making $796

chris · Answer

if the ticket were free, then I would not subtract $4

anonymous · Answer

Thank you so much that makes sense that you have explained everything to me.

anonymous · Answer

you are a lifesaver!

chris · Answer

no problem! good luck!  just remember - figure out the probabilty of each outcome, how much "value" is gained for each outcome, make sure your probabilities add up to 100%, and then add them all up!

chris · Answer

lol, it is my title =), best of luck!